first thing I do is to multiple all the prices and revenue by 10. it avoids having to work with decimal numbers.

let's be A,B and C the numbers of seats for the tickets costing respectively 12$, 18$ and 24$

we have 12A + 18B + 24C = 10,200

and A + B + C = 600

we know that 1/3 of the tickets sold were at 18$, so 200 seats for a revenue of 200*18$ = 3600

we can replace in our equations

12A + (200*18) + 24C = 10,200

12A + 3,600 + 24C = 10,200

12A + 24C = 10,200 - 3,600

12A + 24C = 6,600

and A + B + C = 600

A + C = 400 therefore A = 400 - C

we can replace in the first equation

12(400 - C) + 24C = 6,600

4,800 - 12C + 24C = 6,600

12C = 1800

C = 150

answer is A

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